Going by the list of ingredients, there's only one long term symptom of the vaccine, and that's an immune response to whatever protein is encoded on the RNA strand. The rest of the vaccine the little globs of fat for housing and delivering said RNA strand, and a solution providing a PH balanced environment to store those globs of fat in over time, all of which are flushed from the body fairly quicklike.
The usual side effects are mostly anaphylactic responses to the ingredients within the vaccine, which you're going to know about fairly quicklike. Basically, if you go a week without any side effects, the likelihood of experiencing anything beyond that are slim to none.